Meaning of Zero Input/State Response

[steve23063]

Hi, can someone explain to me, in simple terms, what zero input and zero state response mean? I know the terms should sort of be self explanatory in that zero input reponse is the response of a system when there's no input but how does that make sense?

This is how I'm imagining it in my head right now:
I have a circuit (ie an amplifier) that's just sitting on a desk with no signals inputted to it. Wouldn't zero-input response always be zero? How can the output of the circuit be a non-zero value if nothings going into it?

Also about the zero-state response...what does that mean exactly? You are inputting something into the amplifier circuit in this case but what's it mean to have zero state?

I hope someone can help, I've been able to do problems since I've learned the general method to solving them but I don't understand what's going on or why I'm doing what I'm doing when I solve my homework problems.

 

[chroot]

Even if the input to a system is zero, the output need not be zero.

What if the system was defined as y(t) = x(t) + 10?

Also, there are a class of systems with so-called "infinite impulse response," that may produce non-zero outputs indefinitely if the input has ever been non-zero.

- Warren

 

[steve23063]

Hmm ok so would that be like the amplifier outputting noise even when there is no inputs? Would that be the zero input response?

I still don't understand the state of the circuit and the zero state reponse.


I never heard about infinite impulse response. That's pretty interesting and I can definitely see why zero input reponse would be relevant in that case.

 

[chroot]

The zero state response is nothing more than the response of the circuit when its initial state is taken to be zero. This means that no non-zero input has ever been applied to the system.

If you have a specific homework problem you need help with, it might be better to just post it and tell us where you're stuck.

- Warren

 

[SGT]

First of all, you must understand that zero input and zero state responses refer to the behaviour of dynamic systems.
A dynamic system is a system that has some elements with memory, elements whose stored energy cannot change instantaneously, like capacitors, inductors, masses, springs.
In such a system, the complete response is due to the initial state and to the inputs.
The zero input response depends only on the initial conditions. Think of a charged capacitor discharging through a resistor.
The zero state response depends only on the inputs. Think of a discharged capacitor being charged by a voltage source through a resistor.
An amplifier is not a dynamic system, so if there is no input there is no output.

 

[steve23063]

Ohh I think i get it now. So zero state response would be like if you had an RLC circuit with no energy contained in the inductor or capacitor yet (because the circuit hasn't been used yet) but you start feeding the circuit some input signal. Zero input response would when you have energy contained in the capacitor and inductor (due to something that was inputted to the system at a previous time) but nothing is inputted. Is that correct now the way I'm thinking about it?

Also, even something as simple as a wire and resistor has some capacitance so wouldn't every type of circuit still have a zero state and input response associated with it?

 

[chroot]

You got it, steve.

- Warren

 

[SGT]

Ohh I think i get it now. So zero state response would be like if you had an RLC circuit with no energy contained in the inductor or capacitor yet (because the circuit hasn't been used yet) but you start feeding the circuit some input signal. Zero input response would when you have energy contained in the capacitor and inductor (due to something that was inputted to the system at a previous time) but nothing is inputted. Is that correct now the way I'm thinking about it?

That's it!

Also, even something as simple as a wire and resistor has some capacitance so wouldn't every type of circuit still have a zero state and input response associated with it?

Any physical system has too much characteristics to be analysed in all it's details. That's why we use models.
A model is a simplification of the system that only takes in consideration the properties of the system that are meaningful for the analysis.
For instance, there is no such thing as a linear time invariant element, but if the amplitude of the variations are small enough, we can model the element as linear and if the time involved is small compared with the dynamics of the element, we can model it as time invariant.
The capacitance and inductance of a wire or a resistor are so small, that they can be neglected in almost all applications. Only if you are dealing with microwaves will you need to take them in consideration.

 

[saswatt]

Awesome discussion, i had the same doubt... now cleared.. Thanks a lot to all :)